MHD simulations of flux rope formation and eruption

In this thesis, we study magnetic flux rope (MFR) formation and eruption driven by photospheric converging motion. Two-and-a-half-dimensional magnetohydrodynamics (MHD) simulation and forward modelling analysis are conducted.

Chapter 1 introduces general research background. In Section 1.1, the structure and evolution of the Sun, the solar radiation feature, and the properties of solar magnetic fields are summarised. Section 1.2 reviews research advances in coronal mass ejections (CMEs), flares and prominences. Section 1.3 briefly reviews the basic concepts of magnetic reconnection.

In Chapter 2, the theoretical basis of MHD and numerical methods are revisited. We derive MHD equations in Section 2.1. The starting point is the Hamiltonian equations of particles. Liouville’s theorem is derived from the Hamiltonian equations, then plasma kinetic equations are constructed through BBGKY hierarchy, and finally the magnetohydrodynamics equations are obtained by momentum averages. The numerical methods for computational MHD are introduced in Section 2.2.

In Chapter 3, a two-and-a-half-dimensional MHD simulation is conducted in a chromosphere-transition-corona setup. The initial arcade-like linear force-free magnetic field is driven by an imposed slow motion converging towards the magnetic inversion line at the bottom boundary. The converging motion brings opposite-polarity magnetic flux to the polarity inversion, which leads to the formation of an MFR by magnetic reconnection. The MFR eventually erupts to become a CME. An embedded prominence also gets formed by levitation of chromospheric material during the MFR formation process. Our study shows that the photospheric converging motion is a potential mechanism for MFR formation and a possible triggering mechanism for CMEs. The thermal, dynamical, and magnetic properties of the MFR and its embedded prominence are investigated by tracking their thermal evolution, analyzing their force balance, and measuring their kinematic quantities. The MFR is observed to go through the initiation phase to the acceleration pase in this simulation. The MFR undergoes a series of quasi-static equilibrium states in the initiation phase; while in the acceleration phase the MFR is driven by Lorentz force and the impulsive acceleration occurs. The reconnection mechanism changes from the Sweet-Parker to the unsteady bursty regime of reconnection when the phase transition occurs.

In Chapter 4, we then conduct forward modelling analysis based on MHD simulation of MFR eruption. In the forward modeling analysis, the coronal and chromospheric plasmas are assumed to be in local thermal equilibrium, then the relative populations of the various atomic levels are obtained by solving the Saha equation based on the temperature and density obtained from the MHD simulation. The EUV emission coefficients are proportional to the electron number density squared. The cool and dense plasma is considered to be optically
thick, where the absorption is due to photoionization of neutral hydrogen and neutral and once-ionized helium. Due to the lack of non-thermal particles in MHD simulation, only thermal X-ray emission is calculated based on the optically thin thermal bremsstrahlung model. The CS evolution during MFR eruption can be divided into four stages. The first stage shows the CS to form and gradually lengthen with a low reconnection rate. Resistive instabilities that disrupt the CS mark the beginning of the second stage, and the magnetic reconnection rate increases drastically. Magnetic islands disappear in the third stage accompanied by a low reconnection rate, and reappear in the fourth stage together with a high reconnection rate. Synthetic images and light curves of the seven Solar Dynamics Observatory (SDO)/AIA channels, i.e., 94Å, 131Å, 171Å, 193Å, 211Å, 304Å, and 335Å, and the 3 − 25 keV thermal X-ray are obtained with forward modelling analysis. The loop-top source and the coronal sources of the soft X-ray are reproduced in forward modeling. The light curves of the seven SDO/AIA channels start to rise once resistive instabilities develop. The light curve of the 3 − 25 keV thermal X-ray starts to go up when the reconnection rate reaches one of its peaks. Quasiperiodic pulsations (QPPs) appear twice in the SDO/AIA 171Å, 211Å, and 304Å channels, corresponding to the period of chaotic (re)appearance and CS-guided displacements of the magnetic islands. QPPs appear once in the SDO/AIA 94Å and 335Å channels after the disruption of the CS by resistive instabilities and in the 193Å channel when the chaotic motion of the magnetic islands reappears.

Chapter 5 summarises the thesis and outlooks for the future.